Even a pair of neurons connected via a single synapse -- the simplest constituent of a living nervous system viewed as a network -- is capable of complex behavior. Such a preparation can be modeled at many different levels, but not all models exhibit the full range of behaviors of the original system. We tested several models of the prototypical inhibitory synapse in the crayfish slowly adapting stretch receptor organ (SAO). Simple leaky integrator models, even when significantly modified, exhibit some of the SAO dynamics, but not the full complexity. A hysiological model based on ionic mechanisms identified experimentally provides remarkable duplication of almost all SAO behaviors. We conclude that a reasonable degree of model complexity is necessary for duplication of the basic qualitative dynamics of simple living preparations, and that such models need not be significantly more difficult to analyze than their simpler nonlinear dynamical brethren